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Ternary Operations as Primitive Notions for Constructive Plane Geometry VI
Author(s) -
Pambuccian Victor
Publication year - 1995
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19950410310
Subject(s) - mathematics , euclidean geometry , constructive , axiom , ternary operation , plane (geometry) , non euclidean geometry , algebra over a field , geometry , pure mathematics , discrete mathematics , combinatorics , computer science , process (computing) , programming language , operating system
In this paper we provide quantifier‐free, constructive axiomatizations for several fragments of plane Euclidean geometry over Euclidean fields, such that each axiom contains at most 4 variables. The languages in which they are expressed contain only at most ternary operations. In some precisely defined sense these axiomatizations are the simplest possible.